Interesting discussion. FWIW I've always thought about awase as "pressure" between two moving/fluid things. As one moves in the "pressure" causes the other to move so as to "equalize" the pressure. So sort of blending, sort of aiki, but in a very real way about learning how each movement in essence "causes" the next. It is more about process and moving from one position to the next. Action and reaction in a continuum.

Then again it might just be because I'm not into oscilliscopes and I glaze over whenever stuff like waves get mentioned... And my experience being on a ranch watching my Australian Shepherds move flocks of sheep by adjusting their position and moving subtly towards them causing the flock to move in response which causes the dog to move again etc. Eventually the aussies move the herd where they need to go. But never by charging in, never by racing around, just ideally by a very graceful movement causing "pressure" on the "bubble" around the herd... Cool stuff.

I also think one major lesson in it is about control. Not in the sense of not getting wild, but it creates an extended "conflict" of sorts and one goal is for both to remain in control of the conflict the entire time. Back to my dogs, never letting it get out of control. Both moving forward but also not going too fast or too far such that one of the sheep panics and breaks off (losing control of the whole). Control. Moving in while not creating an opening that you can't also adjust to if that opening is taken.